Divide the following complex numbers: $\dfrac{8(\cos(\frac{7}{4}\pi) + i \sin(\frac{7}{4}\pi))}{\cos(\frac{19}{12}\pi) + i \sin(\frac{19}{12}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $8(\cos(\frac{7}{4}\pi) + i \sin(\frac{7}{4}\pi))$ ) has angle $\frac{7}{4}\pi$ and radius 8. The second number ( $\cos(\frac{19}{12}\pi) + i \sin(\frac{19}{12}\pi)$ ) has angle $\frac{19}{12}\pi$ and radius 1. The radius of the result will be $\frac{8}{1}$ , which is 8. The angle of the result is $\frac{7}{4}\pi - \frac{19}{12}\pi = \frac{1}{6}\pi$ The radius of the result is $8$ and the angle of the result is $\frac{1}{6}\pi$.